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Q.   Judge the equivalent resistance when the following are connected in parallel –

             (a)\; 1\; \Omega \; and \; 10^{6}\Omega        (b)\; 1\; \Omega \; and \; 10^{3}\Omega,\; and \; 10^{6}\Omega,

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(a)\; 1\; \Omega \; and \; 10^{6}\Omega

    R=Equivalent  resistance

    \frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2} 

\Rightarrow \frac{1}{R}=\frac{1}{1}+\frac{1}{10^{6}}

\Rightarrow \frac{1}{R}=\frac{10^6+1}{10^{6}}

\Rightarrow R=\frac{10^6}{10^{6}+1}\approx 1\Omega

(b)\; 1\; \Omega \; and \; 10^{3}\Omega,\; and \; 10^{6}\Omega,

    R=Equivalent  resistance

    \frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} 

\Rightarrow \frac{1}{R}=\frac{1}{1}+\frac{1}{10^3}+\frac{1}{10^{6}}

\Rightarrow \frac{1}{R}=\frac{10^6+10^3+1}{10^{6}}

\Rightarrow R=\frac{10^6}{10^{6}+10^3+1}=0.999\Omega \approx 1\Omega

 

 

 

 

 

 

Posted by

seema garhwal

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